Environmental Engineering Reference
In-Depth Information
60
Start of desaturation of clayey silt
Clayey silt
50
Start of
desaturation
fo fine sand
40
30
20
Fine sand
10
0
1
10
100
1000
Matric suction (
u
a
-
u
w
), kPa
(a) Typical SWCCs
10
-4
Fine sand
10
-5
Permeability function
10
-6
n
sand
Clayey silt
10
-7
10
-8
n
clayey silt
Gardner's equation
k
s
k
w
=
10
-9
n
(
(
u
a
-
u
w
)
w
g
1
a
+
ρ
10
-10
0
100
200
300
400
500
600
Matric suction (
u
a
-
u
w
), kPa
(b) Typical water permeability function
Figure 8.2
Relationship between SWCCs and permeability function for sand and clayey silt
plotted as log-log function.
Similarly, gravimetric water content
w
can be referenced
to zero water content to give a dimensionless water content
d
that can be written as follows:
The effective degree of saturation defined by Brooks and
Corey (1964) normalized the amount of water in a soil
between saturated soil conditions and the residual degree
of saturation:
m
w
/m
p
m
ws
/m
p
=
w
w
s
=
m
w
m
ws
=
V
w
ρ
w
V
v
ρ
w
=
V
w
V
v
=
S
−
S
r
d
=
S
(8.2)
S
e
=
(8.3)
1
.
0
−
S
r
where:
where:
S
e
=
effective degree of saturation,
w
s
=
saturated gravimetric water content,
=
1.0
saturation of the soil, and
m
w
=
mass of water,
S
r
=
residual degree of saturation.
m
p
=
mass of soil particles,
m
ws
=
mass of water when the soil is saturated, and
Volumetric water content
θ
can also be written in a nor-
malized form:
ρ
w
=
density of water.
θ
−
θ
r
n
=
(8.4)
Equations 8.1 and 8.2 indicate that the dimensionless
(gravimetric or volumetric) water contents are identical to
the degree of saturation when water contents range between
dry soil conditions and the saturated water content, provided
the overall soil structure volume change is negligible when
soil suction is changed.
θ
s
−
θ
r
where:
n
=
normalized volumetric water content,
θ
s
=
saturated volumetric water content, and
θ
r
=
residual volumetric water content.
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